Known 355-digit prime factors of googolduplex − 1

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2. Number Theory
3. Known 355-digit prime factors of googolduplex − 1

This is a list of known 355-digit prime factors of googolduplex − 1, i.e., 10^{10^(10^100)} − 1.

These numbers have the form 1 + 2k × 2^m × 5ⁿ, where 0 ≤ m ≤ 10¹⁰⁰ and 0 ≤ m ≤ 10¹⁰⁰.

In the list you can see the prime factors, their discoverer and their corresponding value of k.

1. 25684 3770104377 0532579707 8868488194 1640463275 6139712012 4663624981 1229346927 0401736099 9232129283 3207743142 2444642876 9988380894 5501697421 2929948891 7559738096 7821882477 9005399761 0115743555 0703667104 2442321777 3437500000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=327)
2. 35345 4729501436 3118228955 8075901184 6294215516 8999603686 8803153643 7471578339 9635416651 2704765068 7900563957 2171526894 9525294809 0139950579 7610021410 6733584536 8562223593 4411100588 5480381039 0876606106 7581176757 8125000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=9)
3. 42265 2219442096 0592998778 1200394440 1756986101 6871572281 6935481474 6229714520 9252592244 6099513148 6699055100 7848816030 0922092983 4889720115 8596205261 0382525204 7536462057 7533639301 0421656490 9421295388 6172946273 0599433418 4790586286 4320275711 6463148791 6713588257 4814467120 3762601230 3803690883 7966620922 0886230468 7500000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)